Generating Non-Classical Measurements on Devices with Parameterized Time Evolution

ABSTRACT

A quantum contextual measurement is generated from a quantum device capable of performing continuous time evolution, by generating a first measurement result and a second measurement result and combining the first measurement result and the second measurement result to generate the quantum contextual measurement. The first measurement result may be generated by initializing the quantum device to a first initial quantum state, applying a first continuous time evolution to the first initial state to generate a first evolved state, and measuring the first evolved state to generate the first measurement result. A similar process may be applied to generate a second evolved state which is at least approximately equal to the first evolved state, and then applying another continuous time evolution to the second evolved state to generate a third evolved state, and measuring the third evolved state to generate the second measurement result.

BACKGROUND

The ability for quantum computers to generate non-classical states is,by definition, necessary to create quantum advantage. Because ofengineering constraints limiting the hardware of many of today's quantumcomputers, generating non-classical states on devices can be difficult.In many cases, it can be difficult to verify if the quantum device iseven producing an output which is truly quantum.

Quantum contextuality is an information-theoretic resource which isnecessary for the performance of quantum computers to outperformclassical computers. The presence of quantum contextuality in a dataset,therefore, is an indicator of the generation of non-classical states.Since the advantage of quantum generative machine learning modelsdepends on the ability to generate non-classical states, states whichexhibit quantum contextuality are sufficient to exhibit such a property.

In particular, quantum annealers and other analog quantum computerswhich rely on time evolution, rather than quantum gates, have difficultygenerating states which exhibit certifiable quantum contextuality. Gatemodel quantum computers, for instance, can often certify quantumcontextuality merely by measuring an entangled state in various bases.However, devices which rely on time evolution may be limited in theirability to measure in other bases; for example, modern quantum annealerscan only measure in the Z-basis, which precludes running quantumalgorithms, such as VQE.

SUMMARY

A quantum contextual measurement is generated from a quantum devicecapable of performing continuous time evolution, by generating a firstmeasurement result and a second measurement result and combining thefirst measurement result and the second measurement result to generatethe quantum contextual measurement. The first measurement result may begenerated by initializing the quantum device to a first initial quantumstate, applying a first continuous time evolution to the first initialstate to generate a first evolved state, and measuring the first evolvedstate to generate the first measurement result. A similar process may beapplied to generate a second evolved state which is at leastapproximately equal to the first evolved state, and then applyinganother continuous time evolution to the second evolved state togenerate a third evolved state, and measuring the third evolved state togenerate the second measurement result.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a quantum computer according to one embodiment ofthe present invention;

FIG. 2A is a flowchart of a method performed by the quantum computer ofFIG. 1 according to one embodiment of the present invention;

FIG. 2B is a diagram of a hybrid quantum-classical computer whichperforms quantum annealing according to one embodiment of the presentinvention;

FIG. 3 is a diagram of a hybrid quantum-classical computer according toone embodiment of the present invention;

FIG. 4 is a flowchart of a hybrid quantum-classical computer (HQC)generating a non-classical measurement according to one embodiment ofthe present invention; and

FIG. 5 illustrates the time evolution of an observable in two differentparameter settings according to one embodiment of the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention are directed toward a method ofgenerating measurements that exhibit quantum contextuality. Referring toFIG. 4 , a flow diagram is shown of a method 400, implemented accordingto one embodiment of the present invention, for generating anon-classical measurement. The method 400 comprises initializing 406 aquantum device (which may, for example, be or include the quantumcomputer 102 of FIG. 1 or the hybrid quantum-classical computer 300 ofFIG. 3 ) to create a first initial quantum state 408 |ψ₀

. The method 400 further includes applying 410 a first continuous timeevolution (also referred to as evolving under a Hamiltonian H₁) to theinitial quantum state 408 |ψ₀

to create a first evolved state 412 |ψ₁

. The method 400 further includes measuring 414 the first evolved state412 |ψ₁

to generate a first measurement result {right arrow over (n₁)} 416.

The method 400 again initializes 418 the quantum device to create asecond initial quantum state 420. The method 400 time evolves 422 thesecond initial quantum state 420 to create a second evolved state 424which is at least approximately equal to the first evolved state 412 |ψ₁

.

The method applies 426 a third continuous time evolution (evolving undera second Hamiltonian H₂) to the second evolved state 424 to create athird evolved state 428 |ψ₂

. The method 400 measures 430 the third evolved state 428 |ψ₂

to generate a second measurement result {right arrow over (n₂)} 432. Themethod 400 combines 434 the two measurement results—for example, byconcatenating the first measurement result 416 {right arrow over (n₁)}with the second measurement result 432 {right arrow over (n₂)}—to form acomplete measurement {right arrow over (m)} 436.

Embodiments of the present invention may use any of a plurality ofparameterized time evolutions and measurements, in any of a variety ofcombinations. For example, consider an n-qubit quantum system with acontrollable and parameterized time-dependent evolution under aHamiltonian H(t, x) where x is a set of parameters. Define the state ofthe system as |ψ(t, x)

for time t and parameter setting x. Embodiments of the present inventionemploy a measurement at a certain time t_(i), and the information gainedfrom each measurement is an n-bit string, denoted {right arrow over(n)}_(i). One or more additional measurements at different times t_(i)which, when combined, may form a sample of n·k=m bits, where k is thetotal number of measurements.

Embodiments of the present invention include systems and methods forusing a plurality of measurements to perform variational optimization.In typical gate-model variational optimization schemes, measurements ofan output quantum state are used as arguments for an objective function;the value of the objective function then provides feedback to anoptimization routine which suggests new values for parameters of themodel, i.e., parameters defining quantum gates generating the outputquantum state. The process is repeated until the optimization routecompletes, wherein a maximum or minimum value of the objective functionis identified. Similarly, embodiments of the present invention may useparameterized time evolution under a parameterized Hamiltonian H(t, x),where the resulting measurement {right arrow over (m)} is used as anargument for the objective function and the parameter x is updated basedon the optimization routine (see FIG. 5 ).

Embodiments of the present invention include utilizing the generatednon-classical measurements as inputs for a quantum generator in machinelearning models. For example, let H(t, x) be such that H₁(t, x) for time0≤t≤t₀ for some t₀ and H₂(t) for time t₀≤t≤T. Let |ψ₁

=|ψ(t₀, x)) be the state at time t₀ and |ψ₂

=|ψ(T, x)

be the state at time T. Since H₂ is independent of x, |ψ₁

and |ψ₂

differ by a unitary operation U that is independent of x. Suppose eachof |ψ₁

and |ψ₂

are measured in the Z basis, generating a total of m=2 n bits. In thecase where UZ^(⊗n)U^(†) is not co-measurable with Z^(†n), the m-bitsample comes from a probability distribution that embodies quantumcontextuality that does not have classical analogues. This capabilitycan be useful for quantum-enhanced generative modeling where the samplesderived from the quantum device act as latent space inputs that aremapping to a data space by a machine learning model such as neuralnetworks. The variable x can be used as an adjustable parameter by theneural network to train the model; meanwhile, samples retain theirproperty of quantum contextuality. It is believed that non-classicalstates are required for quantum generative models to provide a quantumadvantage over classical generative models. Since quantum contextualityis a sufficient condition for the generation of non-classical states,embodiments of the present invention may outperform quantum generativelearning models whose inputs do not possess (or cannot be certified topossess) quantum contextuality.

Advantages of embodiments of the present invention apply, for example,to quantum devices which utilize parameterized time evolution instead ofquantum gates. This is particularly useful when the number ofmeasurement bases in limited in the quantum device. Consider, forexample, a quantum annealer which can measure only in the Z-basis andimplements the Hamiltonian H₁(t, x). However, as earlier described,embodiments of the present invention can generate measurements describedvia a unitary rotation which, for particular choices of U, is equivalentto measuring the state in the implemented Hamiltonian H₁(t, x) inanother basis (e.g. the X basis). Thus, embodiments of the presentinvention enable new measurements to be taken on quantum annealerswithout requiring modifications to the hardware. Embodiments of thepresent invention may also be utilized in devices other than quantumannealers. For example, quantum devices whose qubits manifest in neutralatoms (sometimes referred to as analog quantum computers or analogquantum simulators) also utilize parameterized time evolution.

Embodiments of the present invention include performing measurements ina plurality of bases. For example, embodiments of the present inventionmay repeat the preparation of state |ψ₁

and apply a continuous time evolution H_(j)(t) corresponding toappropriate basis-changing unitary U_(j). All such resultingmeasurements {right arrow over (n_(j))} may then be combined to form{right arrow over (m)}.

Embodiments of the present invention include certifying the generatedmeasurements as exhibiting quantum contextuality. The combination of aset of measurements, for example, may be certified by demonstrating theviolation of a Bell inequality, e.g., by the method of [Frerot andRoscilde, https://arxiv.org/pdf/2004.07796.pdf (2021)] which isincorporated by reference herein.

One embodiment of the present invention is directed to a method forgenerating a quantum contextual measurement from a quantum devicecapable of performing continuous time evolution. The method includes:(A) generating a first measurement result, the generating comprising:(A) (1) initializing the quantum device to a first initial quantumstate; (A) (2) applying, on the quantum device, a first continuous timeevolution to the initial quantum state to generate a first evolvedstate; and (A) (3) measuring the first evolved state on the quantumdevice to generate the first measurement result; (B) generating a secondmeasurement result, the generating comprising: (B) (1) initializing thequantum device to a second initial quantum state; (B) (2) applying, onthe quantum device, a second continuous time evolution to the secondinitial quantum state to generate a second evolved state which is atleast approximately equal to the first evolved state; (B) (3) applying,on the quantum device, a third continuous time evolution to the secondevolved state to generate a third evolved state; and (B) (4) measuringthe third evolved state on the quantum device to generate the secondmeasurement result; and (C) combining the first measurement result andthe second measurement result to generate the quantum contextualmeasurement. The second evolved state may be equal to the first evolvedstate.

At least one of the first continuous time evolution and the secondcontinuous time evolution may be parameterized by a set of parameters.The method may further include: (D) providing an input into a generativeneural network, wherein the input is a function of the quantumcontextual measurement. The method may further include: (D) tuning theset of parameters, based on an objective function, to produce an updatedset of parameters.

The second continuous time evolution may be chosen such that measuringthe third evolved state is equivalent to a change of basis on measuringthe first evolved state.

The second continuous time evolution may be equivalent to a change ofbasis on measuring the first evolved state.

The quantum device may comprise a quantum annealer.

The second initial quantum state may be at least approximately equal tothe first initial quantum state. For example, the second initial quantumstate may be equal to the first initial quantum state.

The second continuous time evolution may be at least approximately equalto the first continuous time evolution. For example, the secondcontinuous time evolution may be equal to the first continuous timeevolution.

The method may further include: (D) generating a plurality of additionalmeasurement results, wherein the generation of each additionalmeasurement results comprises: (D) (1) initializing the quantum deviceto an additional initial quantum state; (D) (2) applying, on the quantumdevice, a first additional continuous time evolution to the additionalinitial quantum state to generate a first additional evolved state whichis at least approximately equal to the first evolved state; (D) (3)applying, on the quantum device, a second additional continuous timeevolution to the first additional evolved state to generate a secondadditional evolved state; and (D) (4) measuring the second additionalevolved state on the quantum device to generate the additionalmeasurement result; and (E) combining the plurality of additionalmeasurement results to the quantum contextual measurement to generate anexpanded quantum contextual measurement.

Another embodiment of the present invention is directed to a hybridquantum-classical computing system for generating a quantum contextualmeasurement from a quantum device capable of performing continuous timeevolution. The hybrid quantum-classical computing system includes: thequantum device, comprising a plurality of qubits and a qubit controllerthat manipulates the plurality of qubits; and a classical computerincluding at least one processor and at least one non-transitorycomputer-readable medium, the at least one non-transitorycomputer-readable medium having computer program instructions storedthereon, the computer program instructions being executable by the atleast one processor to cause the classical computer to cooperate withthe quantum device to perform a method. The method includes: (A)generating a first measurement result, the generating comprising: (A)(1) initializing the quantum device to a first initial quantum state;(A) (2) applying, on the quantum device, a first continuous timeevolution to the initial quantum state to generate a first evolvedstate; and (A) (3) measuring the first evolved state on the quantumdevice to generate the first measurement result; (B) generating a secondmeasurement result, the generating comprising: (B) (1) initializing thequantum device to a second initial quantum state; (B) (2) applying, onthe quantum device, a second continuous time evolution to the secondinitial quantum state to generate a second evolved state which is atleast approximately equal to the first evolved state; (B) (3) applying,on the quantum device, a third continuous time evolution to the secondevolved state to generate a third evolved state; and (B) (4) measuringthe third evolved state on the quantum device to generate the secondmeasurement result; and (C) combining the first measurement result andthe second measurement result to generate the quantum contextualmeasurement. The second evolved state may be equal to the first evolvedstate.

It is to be understood that although the invention has been describedabove in terms of particular embodiments, the foregoing embodiments areprovided as illustrative only, and do not limit or define the scope ofthe invention. Various other embodiments, including but not limited tothe following, are also within the scope of the claims. For example,elements and components described herein may be further divided intoadditional components or joined together to form fewer components forperforming the same functions.

Various physical embodiments of a quantum computer are suitable for useaccording to the present disclosure. In general, the fundamental datastorage unit in quantum computing is the quantum bit, or qubit. Thequbit is a quantum-computing analog of a classical digital computersystem bit. A classical bit is considered to occupy, at any given pointin time, one of two possible states corresponding to the binary digits(bits) 0 or 1. By contrast, a qubit is implemented in hardware by aphysical medium with quantum-mechanical characteristics. Such a medium,which physically instantiates a qubit, may be referred to herein as a“physical instantiation of a qubit,” a “physical embodiment of a qubit,”a “medium embodying a qubit,” or similar terms, or simply as a “qubit,”for ease of explanation. It should be understood, therefore, thatreferences herein to “qubits” within descriptions of embodiments of thepresent invention refer to physical media which embody qubits.

Each qubit has an infinite number of different potentialquantum-mechanical states. When the state of a qubit is physicallymeasured, the measurement produces one of two different basis statesresolved from the state of the qubit. Thus, a single qubit can representa one, a zero, or any quantum superposition of those two qubit states; apair of qubits can be in any quantum superposition of 4 orthogonal basisstates; and three qubits can be in any superposition of 8 orthogonalbasis states. The function that defines the quantum-mechanical states ofa qubit is known as its wavefunction. The wavefunction also specifiesthe probability distribution of outcomes for a given measurement. Aqubit, which has a quantum state of dimension two (i.e., has twoorthogonal basis states), may be generalized to a d-dimensional “qudit,”where d may be any integral value, such as 2, 3, 4, or higher. In thegeneral case of a qudit, measurement of the qudit produces one of ddifferent basis states resolved from the state of the qudit. Anyreference herein to a qubit should be understood to refer more generallyto an d-dimensional qudit with any value of d.

Although certain descriptions of qubits herein may describe such qubitsin terms of their mathematical properties, each such qubit may beimplemented in a physical medium in any of a variety of different ways.Examples of such physical media include superconducting material,trapped ions, photons, optical cavities, individual electrons trappedwithin quantum dots, point defects in solids (e.g., phosphorus donors insilicon or nitrogen-vacancy centers in diamond), molecules (e.g.,alanine, vanadium complexes), or aggregations of any of the foregoingthat exhibit qubit behavior, that is, comprising quantum states andtransitions therebetween that can be controllably induced or detected.

For any given medium that implements a qubit, any of a variety ofproperties of that medium may be chosen to implement the qubit. Forexample, if electrons are chosen to implement qubits, then the xcomponent of its spin degree of freedom may be chosen as the property ofsuch electrons to represent the states of such qubits. Alternatively,the y component, or the z component of the spin degree of freedom may bechosen as the property of such electrons to represent the state of suchqubits. This is merely a specific example of the general feature thatfor any physical medium that is chosen to implement qubits, there may bemultiple physical degrees of freedom (e.g., the x, y, and z componentsin the electron spin example) that may be chosen to represent 0 and 1.For any particular degree of freedom, the physical medium maycontrollably be put in a state of superposition, and measurements maythen be taken in the chosen degree of freedom to obtain readouts ofqubit values.

Certain implementations of quantum computers, referred as gate modelquantum computers, comprise quantum gates. In contrast to classicalgates, there is an infinite number of possible single-qubit quantumgates that change the state vector of a qubit. Changing the state of aqubit state vector typically is referred to as a single-qubit rotation,and may also be referred to herein as a state change or a single-qubitquantum-gate operation. A rotation, state change, or single-qubitquantum-gate operation may be represented mathematically by a unitary2×2 matrix with complex elements. A rotation corresponds to a rotationof a qubit state within its Hilbert space, which may be conceptualizedas a rotation of the Bloch sphere. (As is well-known to those havingordinary skill in the art, the Bloch sphere is a geometricalrepresentation of the space of pure states of a qubit.) Multi-qubitgates alter the quantum state of a set of qubits. For example, two-qubitgates rotate the state of two qubits as a rotation in thefour-dimensional Hilbert space of the two qubits. (As is well-known tothose having ordinary skill in the art, a Hilbert space is an abstractvector space possessing the structure of an inner product that allowslength and angle to be measured. Furthermore, Hilbert spaces arecomplete: there are enough limits in the space to allow the techniquesof calculus to be used.)

A quantum circuit may be specified as a sequence of quantum gates. Asdescribed in more detail below, the term “quantum gate,” as used herein,refers to the application of a gate control signal (defined below) toone or more qubits to cause those qubits to undergo certain physicaltransformations and thereby to implement a logical gate operation. Toconceptualize a quantum circuit, the matrices corresponding to thecomponent quantum gates may be multiplied together in the orderspecified by the gate sequence to produce a 2n×2n complex matrixrepresenting the same overall state change on n qubits. A quantumcircuit may thus be expressed as a single resultant operator. However,designing a quantum circuit in terms of constituent gates allows thedesign to conform to a standard set of gates, and thus enable greaterease of deployment. A quantum circuit thus corresponds to a design foractions taken upon the physical components of a quantum computer.

A given variational quantum circuit may be parameterized in a suitabledevice-specific manner. More generally, the quantum gates making up aquantum circuit may have an associated plurality of tuning parameters.For example, in embodiments based on optical switching, tuningparameters may correspond to the angles of individual optical elements.

In certain embodiments of quantum circuits, the quantum circuit includesboth one or more gates and one or more measurement operations. Quantumcomputers implemented using such quantum circuits are referred to hereinas implementing “measurement feedback.” For example, a quantum computerimplementing measurement feedback may execute the gates in a quantumcircuit and then measure only a subset (i.e., fewer than all) of thequbits in the quantum computer, and then decide which gate(s) to executenext based on the outcome(s) of the measurement(s). In particular, themeasurement(s) may indicate a degree of error in the gate operation(s),and the quantum computer may decide which gate(s) to execute next basedon the degree of error. The quantum computer may then execute thegate(s) indicated by the decision. This process of executing gates,measuring a subset of the qubits, and then deciding which gate(s) toexecute next may be repeated any number of times. Measurement feedbackmay be useful for performing quantum error correction, but is notlimited to use in performing quantum error correction. For every quantumcircuit, there is an error-corrected implementation of the circuit withor without measurement feedback.

Some embodiments described herein generate, measure, or utilize quantumstates that approximate a target quantum state (e.g., a ground state ofa Hamiltonian). As will be appreciated by those trained in the art,there are many ways to quantify how well a first quantum state“approximates” a second quantum state. In the following description, anyconcept or definition of approximation known in the art may be usedwithout departing from the scope hereof. For example, when the first andsecond quantum states are represented as first and second vectors,respectively, the first quantum state approximates the second quantumstate when an inner product between the first and second vectors (calledthe “fidelity” between the two quantum states) is greater than apredefined amount (typically labeled ε). In this example, the fidelityquantifies how “close” or “similar” the first and second quantum statesare to each other. The fidelity represents a probability that ameasurement of the first quantum state will give the same result as ifthe measurement were performed on the second quantum state. Proximitybetween quantum states can also be quantified with a distance measure,such as a Euclidean norm, a Hamming distance, or another type of normknown in the art. Proximity between quantum states can also be definedin computational terms. For example, the first quantum stateapproximates the second quantum state when a polynomial time-sampling ofthe first quantum state gives some desired information or property thatit shares with the second quantum state.

Not all quantum computers are gate model quantum computers. Embodimentsof the present invention are not limited to being implemented using gatemodel quantum computers. As an alternative example, embodiments of thepresent invention may be implemented, in whole or in part, using aquantum computer that is implemented using a quantum annealingarchitecture, which is an alternative to the gate model quantumcomputing architecture. More specifically, quantum annealing (QA) is ametaheuristic for finding the global minimum of a given objectivefunction over a given set of candidate solutions (candidate states), bya process using quantum fluctuations.

FIG. 2B shows a diagram illustrating operations typically performed by acomputer system 250 which implements quantum annealing. The system 250includes both a quantum computer 252 and a classical computer 254.Operations shown on the left of the dashed vertical line 256 typicallyare performed by the quantum computer 252, while operations shown on theright of the dashed vertical line 256 typically are performed by theclassical computer 254.

Quantum annealing starts with the classical computer 254 generating aninitial Hamiltonian 260 and a final Hamiltonian 262 based on acomputational problem 258 to be solved, and providing the initialHamiltonian 260, the final Hamiltonian 262 and an annealing schedule 270as input to the quantum computer 252. The quantum computer 252 preparesa well-known initial state 266 (FIG. 2B, operation 264), such as aquantum-mechanical superposition of all possible states (candidatestates) with equal weights, based on the initial Hamiltonian 260. Theclassical computer 254 provides the initial Hamiltonian 260, a finalHamiltonian 262, and an annealing schedule 270 to the quantum computer252. The quantum computer 252 starts in the initial state 266, andevolves its state according to the annealing schedule 270 following thetime-dependent Schrödinger equation, a natural quantum-mechanicalevolution of physical systems (FIG. 2B, operation 268). Morespecifically, the state of the quantum computer 252 undergoes timeevolution under a time-dependent Hamiltonian, which starts from theinitial Hamiltonian 260 and terminates at the final Hamiltonian 262. Ifthe rate of change of the system Hamiltonian is slow enough, the systemstays close to the ground state of the instantaneous Hamiltonian. If therate of change of the system Hamiltonian is accelerated, the system mayleave the ground state temporarily but produce a higher likelihood ofconcluding in the ground state of the final problem Hamiltonian, i.e.,diabatic quantum computation. At the end of the time evolution, the setof qubits on the quantum annealer is in a final state 272, which isexpected to be close to the ground state of the classical Ising modelthat corresponds to the solution to the original optimization problem258. An experimental demonstration of the success of quantum annealingfor random magnets was reported immediately after the initialtheoretical proposal.

The final state 272 of the quantum computer 254 is measured, therebyproducing results 276 (i.e., measurements) (FIG. 2B, operation 274). Themeasurement operation 274 may be performed, for example, in any of theways disclosed herein, such as in any of the ways disclosed herein inconnection with the measurement unit 110 in FIG. 1 . The classicalcomputer 254 performs postprocessing on the measurement results 276 toproduce output 280 representing a solution to the original computationalproblem 258 (FIG. 2B, operation 278).

As yet another alternative example, embodiments of the present inventionmay be implemented, in whole or in part, using a quantum computer thatis implemented using a one-way quantum computing architecture, alsoreferred to as a measurement-based quantum computing architecture, whichis another alternative to the gate model quantum computing architecture.More specifically, the one-way or measurement based quantum computer(MBQC) is a method of quantum computing that first prepares an entangledresource state, usually a cluster state or graph state, then performssingle qubit measurements on it. It is “one-way” because the resourcestate is destroyed by the measurements.

The outcome of each individual measurement is random, but they arerelated in such a way that the computation always succeeds. In generalthe choices of basis for later measurements need to depend on theresults of earlier measurements, and hence the measurements cannot allbe performed at the same time.

Any of the functions disclosed herein may be implemented using means forperforming those functions. Such means include, but are not limited to,any of the components disclosed herein, such as the computer-relatedcomponents described below.

Referring to FIG. 1 , a diagram is shown of a system 100 implementedaccording to one embodiment of the present invention. Referring to FIG.2A, a flowchart is shown of a method 200 performed by the system 100 ofFIG. 1 according to one embodiment of the present invention. The system100 includes a quantum computer 102. The quantum computer 102 includes aplurality of qubits 104, which may be implemented in any of the waysdisclosed herein. There may be any number of qubits 104 in the quantumcomputer 104. For example, the qubits 104 may include or consist of nomore than 2 qubits, no more than 4 qubits, no more than 8 qubits, nomore than 16 qubits, no more than 32 qubits, no more than 64 qubits, nomore than 128 qubits, no more than 256 qubits, no more than 512 qubits,no more than 1024 qubits, no more than 2048 qubits, no more than 4096qubits, or no more than 8192 qubits. These are merely examples, inpractice there may be any number of qubits 104 in the quantum computer102.

There may be any number of gates in a quantum circuit. However, in someembodiments the number of gates may be at least proportional to thenumber of qubits 104 in the quantum computer 102. In some embodimentsthe gate depth may be no greater than the number of qubits 104 in thequantum computer 102, or no greater than some linear multiple of thenumber of qubits 104 in the quantum computer 102 (e.g., 2, 3, 4, 5, 6,or 7).

The qubits 104 may be interconnected in any graph pattern. For example,they be connected in a linear chain, a two-dimensional grid, anall-to-all connection, any combination thereof, or any subgraph of anyof the preceding.

As will become clear from the description below, although element 102 isreferred to herein as a “quantum computer,” this does not imply that allcomponents of the quantum computer 102 leverage quantum phenomena. Oneor more components of the quantum computer 102 may, for example, beclassical (i.e., non-quantum components) components which do notleverage quantum phenomena.

The quantum computer 102 includes a control unit 106, which may includeany of a variety of circuitry and/or other machinery for performing thefunctions disclosed herein. The control unit 106 may, for example,consist entirely of classical components. The control unit 106 generatesand provides as output one or more control signals 108 to the qubits104. The control signals 108 may take any of a variety of forms, such asany kind of electromagnetic signals, such as electrical signals,magnetic signals, optical signals (e.g., laser pulses), or anycombination thereof.

For example:

-   -   In embodiments in which some or all of the qubits 104 are        implemented as photons (also referred to as a “quantum optical”        implementation) that travel along waveguides, the control unit        106 may be a beam splitter (e.g., a heater or a mirror), the        control signals 108 may be signals that control the heater or        the rotation of the mirror, the measurement unit 110 may be a        photodetector, and the measurement signals 112 may be photons.    -   In embodiments in which some or all of the qubits 104 are        implemented as charge type qubits (e.g., transmon, X-mon, G-mon)        or flux-type qubits (e.g., flux qubits, capacitively shunted        flux qubits) (also referred to as a “circuit quantum        electrodynamic” (circuit QED) implementation), the control unit        106 may be a bus resonator activated by a drive, the control        signals 108 may be cavity modes, the measurement unit 110 may be        a second resonator (e.g., a low-Q resonator), and the        measurement signals 112 may be voltages measured from the second        resonator using dispersive readout techniques.    -   In embodiments in which some or all of the qubits 104 are        implemented as superconducting circuits, the control unit 106        may be a circuit QED-assisted control unit or a direct        capacitive coupling control unit or an inductive capacitive        coupling control unit, the control signals 108 may be cavity        modes, the measurement unit 110 may be a second resonator (e.g.,        a low-Q resonator), and the measurement signals 112 may be        voltages measured from the second resonator using dispersive        readout techniques.    -   In embodiments in which some or all of the qubits 104 are        implemented as trapped ions (e.g., electronic states of, e.g.,        magnesium ions), the control unit 106 may be a laser, the        control signals 108 may be laser pulses, the measurement unit        110 may be a laser and either a CCD or a photodetector (e.g., a        photomultiplier tube), and the measurement signals 112 may be        photons.    -   In embodiments in which some or all of the qubits 104 are        implemented using nuclear magnetic resonance (NMR) (in which        case the qubits may be molecules, e.g., in liquid or solid        form), the control unit 106 may be a radio frequency (RF)        antenna, the control signals 108 may be RF fields emitted by the        RF antenna, the measurement unit 110 may be another RF antenna,        and the measurement signals 112 may be RF fields measured by the        second RF antenna.    -   In embodiments in which some or all of the qubits 104 are        implemented as nitrogen-vacancy centers (NV centers), the        control unit 106 may, for example, be a laser, a microwave        antenna, or a coil, the control signals 108 may be visible        light, a microwave signal, or a constant electromagnetic field,        the measurement unit 110 may be a photodetector, and the        measurement signals 112 may be photons.    -   In embodiments in which some or all of the qubits 104 are        implemented as two-dimensional quasiparticles called “anyons”        (also referred to as a “topological quantum computer”        implementation), the control unit 106 may be nanowires, the        control signals 108 may be local electrical fields or microwave        pulses, the measurement unit 110 may be superconducting        circuits, and the measurement signals 112 may be voltages.    -   In embodiments in which some or all of the qubits 104 are        implemented as semiconducting material (e.g., nanowires), the        control unit 106 may be microfabricated gates, the control        signals 108 may be RF or microwave signals, the measurement unit        110 may be microfabricated gates, and the measurement signals        112 may be RF or microwave signals.

Although not shown explicitly in FIG. 1 and not required, themeasurement unit 110 may provide one or more feedback signals 114 to thecontrol unit 106 based on the measurement signals 112. For example,quantum computers referred to as “one-way quantum computers” or“measurement-based quantum computers” utilize such feedback 114 from themeasurement unit 110 to the control unit 106. Such feedback 114 is alsonecessary for the operation of fault-tolerant quantum computing anderror correction.

The control signals 108 may, for example, include one or more statepreparation signals which, when received by the qubits 104, cause someor all of the qubits 104 to change their states. Such state preparationsignals constitute a quantum circuit also referred to as an “ansatzcircuit.” The resulting state of the qubits 104 is referred to herein asan “initial state” or an “ansatz state.” The process of outputting thestate preparation signal(s) to cause the qubits 104 to be in theirinitial state is referred to herein as “state preparation” (FIG. 2A,section 206). A special case of state preparation is “initialization,”also referred to as a “reset operation,” in which the initial state isone in which some or all of the qubits 104 are in the “zero” state i.e.the default single-qubit state. More generally, state preparation mayinvolve using the state preparation signals to cause some or all of thequbits 104 to be in any distribution of desired states. In someembodiments, the control unit 106 may first perform initialization onthe qubits 104 and then perform preparation on the qubits 104, by firstoutputting a first set of state preparation signals to initialize thequbits 104, and by then outputting a second set of state preparationsignals to put the qubits 104 partially or entirely into non-zerostates.

Another example of control signals 108 that may be output by the controlunit 106 and received by the qubits 104 are gate control signals. Thecontrol unit 106 may output such gate control signals, thereby applyingone or more gates to the qubits 104. Applying a gate to one or morequbits causes the set of qubits to undergo a physical state change whichembodies a corresponding logical gate operation (e.g., single-qubitrotation, two-qubit entangling gate or multi-qubit operation) specifiedby the received gate control signal. As this implies, in response toreceiving the gate control signals, the qubits 104 undergo physicaltransformations which cause the qubits 104 to change state in such a waythat the states of the qubits 104, when measured (see below), representthe results of performing logical gate operations specified by the gatecontrol signals. The term “quantum gate,” as used herein, refers to theapplication of a gate control signal to one or more qubits to causethose qubits to undergo the physical transformations described above andthereby to implement a logical gate operation.

It should be understood that the dividing line between state preparation(and the corresponding state preparation signals) and the application ofgates (and the corresponding gate control signals) may be chosenarbitrarily. For example, some or all the components and operations thatare illustrated in FIGS. 1 and 2A-2B as elements of “state preparation”may instead be characterized as elements of gate application.Conversely, for example, some or all of the components and operationsthat are illustrated in FIGS. 1 and 2A-2B as elements of “gateapplication” may instead be characterized as elements of statepreparation. As one particular example, the system and method of FIGS. 1and 2A-2B may be characterized as solely performing state preparationfollowed by measurement, without any gate application, where theelements that are described herein as being part of gate application areinstead considered to be part of state preparation. Conversely, forexample, the system and method of FIGS. 1 and 2A-2B may be characterizedas solely performing gate application followed by measurement, withoutany state preparation, and where the elements that are described hereinas being part of state preparation are instead considered to be part ofgate application.

The quantum computer 102 also includes a measurement unit 110, whichperforms one or more measurement operations on the qubits 104 to readout measurement signals 112 (also referred to herein as “measurementresults”) from the qubits 104, where the measurement results 112 aresignals representing the states of some or all of the qubits 104. Inpractice, the control unit 106 and the measurement unit 110 may beentirely distinct from each other, or contain some components in commonwith each other, or be implemented using a single unit (i.e., a singleunit may implement both the control unit 106 and the measurement unit110). For example, a laser unit may be used both to generate the controlsignals 108 and to provide stimulus (e.g., one or more laser beams) tothe qubits 104 to cause the measurement signals 112 to be generated.

In general, the quantum computer 102 may perform various operationsdescribed above any number of times. For example, the control unit 106may generate one or more control signals 108, thereby causing the qubits104 to perform one or more quantum gate operations. The measurement unit110 may then perform one or more measurement operations on the qubits104 to read out a set of one or more measurement signals 112. Themeasurement unit 110 may repeat such measurement operations on thequbits 104 before the control unit 106 generates additional controlsignals 108, thereby causing the measurement unit 110 to read outadditional measurement signals 112 resulting from the same gateoperations that were performed before reading out the previousmeasurement signals 112. The measurement unit 110 may repeat thisprocess any number of times to generate any number of measurementsignals 112 corresponding to the same gate operations. The quantumcomputer 102 may then aggregate such multiple measurements of the samegate operations in any of a variety of ways.

After the measurement unit 110 has performed one or more measurementoperations on the qubits 104 after they have performed one set of gateoperations, the control unit 106 may generate one or more additionalcontrol signals 108, which may differ from the previous control signals108, thereby causing the qubits 104 to perform one or more additionalquantum gate operations, which may differ from the previous set ofquantum gate operations. The process described above may then berepeated, with the measurement unit 110 performing one or moremeasurement operations on the qubits 104 in their new states (resultingfrom the most recently-performed gate operations).

In general, the system 100 may implement a plurality of quantum circuitsas follows. For each quantum circuit C in the plurality of quantumcircuits (FIG. 2A, operation 202), the system 100 performs a pluralityof “shots” on the qubits 104. The meaning of a shot will become clearfrom the description that follows. For each shot S in the plurality ofshots (FIG. 2A, operation 204), the system 100 prepares the state of thequbits 104 (FIG. 2A, section 206). More specifically, for each quantumgate G in quantum circuit C (FIG. 2A, operation 210), the system 100applies quantum gate G to the qubits 104 (FIG. 2A, operations 212 and214).

Then, for each of the qubits Q 104 (FIG. 2A, operation 216), the system100 measures the qubit Q to produce measurement output representing acurrent state of qubit Q (FIG. 2A, operations 218 and 220).

The operations described above are repeated for each shot S (FIG. 2A,operation 222), and circuit C (FIG. 2A, operation 224). As thedescription above implies, a single “shot” involves preparing the stateof the qubits 104 and applying all of the quantum gates in a circuit tothe qubits 104 and then measuring the states of the qubits 104; and thesystem 100 may perform multiple shots for one or more circuits.

Referring to FIG. 3 , a diagram is shown of a hybrid classical quantumcomputer (HQC) 300 implemented according to one embodiment of thepresent invention. The HQC 300 includes a quantum computer component 102(which may, for example, be implemented in the manner shown anddescribed in connection with FIG. 1 ) and a classical computer component306. The classical computer component may be a machine implementedaccording to the general computing model established by John VonNeumann, in which programs are written in the form of ordered lists ofinstructions and stored within a classical (e.g., digital) memory 310and executed by a classical (e.g., digital) processor 308 of theclassical computer. The memory 310 is classical in the sense that itstores data in a storage medium in the form of bits, which have a singledefinite binary state at any point in time. The bits stored in thememory 310 may, for example, represent a computer program. The classicalcomputer component 304 typically includes a bus 314. The processor 308may read bits from and write bits to the memory 310 over the bus 314.For example, the processor 308 may read instructions from the computerprogram in the memory 310, and may optionally receive input data 316from a source external to the computer 302, such as from a user inputdevice such as a mouse, keyboard, or any other input device. Theprocessor 308 may use instructions that have been read from the memory310 to perform computations on data read from the memory 310 and/or theinput 316, and generate output from those instructions. The processor308 may store that output back into the memory 310 and/or provide theoutput externally as output data 318 via an output device, such as amonitor, speaker, or network device.

The quantum computer component 102 may include a plurality of qubits104, as described above in connection with FIG. 1 . A single qubit mayrepresent a one, a zero, or any quantum superposition of those two qubitstates. The classical computer component 304 may provide classical statepreparation signals Y32 to the quantum computer 102, in response towhich the quantum computer 102 may prepare the states of the qubits 104in any of the ways disclosed herein, such as in any of the waysdisclosed in connection with FIGS. 1 and 2A-2B.

Once the qubits 104 have been prepared, the classical processor 308 mayprovide classical control signals Y34 to the quantum computer 102, inresponse to which the quantum computer 102 may apply the gate operationsspecified by the control signals Y32 to the qubits 104, as a result ofwhich the qubits 104 arrive at a final state. The measurement unit 110in the quantum computer 102 (which may be implemented as described abovein connection with FIGS. 1 and 2A-2B) may measure the states of thequbits 104 and produce measurement output Y38 representing the collapseof the states of the qubits 104 into one of their eigenstates. As aresult, the measurement output Y38 includes or consists of bits andtherefore represents a classical state. The quantum computer 102provides the measurement output Y38 to the classical processor 308. Theclassical processor 308 may store data representing the measurementoutput Y38 and/or data derived therefrom in the classical memory 310.

The steps described above may be repeated any number of times, with whatis described above as the final state of the qubits 104 serving as theinitial state of the next iteration. In this way, the classical computer304 and the quantum computer 102 may cooperate as co-processors toperform joint computations as a single computer system.

Although certain functions may be described herein as being performed bya classical computer and other functions may be described herein asbeing performed by a quantum computer, these are merely examples and donot constitute limitations of the present invention. A subset of thefunctions which are disclosed herein as being performed by a quantumcomputer may instead be performed by a classical computer. For example,a classical computer may execute functionality for emulating a quantumcomputer and provide a subset of the functionality described herein,albeit with functionality limited by the exponential scaling of thesimulation. Functions which are disclosed herein as being performed by aclassical computer may instead be performed by a quantum computer.

The techniques described above may be implemented, for example, inhardware, in one or more computer programs tangibly stored on one ormore computer-readable media, firmware, or any combination thereof, suchas solely on a quantum computer, solely on a classical computer, or on ahybrid classical quantum (HQC) computer. The techniques disclosed hereinmay, for example, be implemented solely on a classical computer, inwhich the classical computer emulates the quantum computer functionsdisclosed herein.

The techniques described above may be implemented in one or morecomputer programs executing on (or executable by) a programmablecomputer (such as a classical computer, a quantum computer, or an HQC)including any combination of any number of the following: a processor, astorage medium readable and/or writable by the processor (including, forexample, volatile and non-volatile memory and/or storage elements), aninput device, and an output device. Program code may be applied to inputentered using the input device to perform the functions described and togenerate output using the output device.

Embodiments of the present invention include features which are onlypossible and/or feasible to implement with the use of one or morecomputers, computer processors, and/or other elements of a computersystem. Such features are either impossible or impractical to implementmentally and/or manually. For example, embodiments of the presentinvention manipulate qubits on a quantum computer, which cannot beperformed mentally or manually by a human. More specifically,embodiments of the present invention apply a continuous time evolution(also referred to as evolving under a Hamiltonian H₁) to an initialquantum state to create an evolved quantum state, which cannot beperformed mentally or manually by a human.

Any claims herein which affirmatively require a computer, a processor, amemory, or similar computer-related elements, are intended to requiresuch elements, and should not be interpreted as if such elements are notpresent in or required by such claims. Such claims are not intended, andshould not be interpreted, to cover methods and/or systems which lackthe recited computer-related elements. For example, any method claimherein which recites that the claimed method is performed by a computer,a processor, a memory, and/or similar computer-related element, isintended to, and should only be interpreted to, encompass methods whichare performed by the recited computer-related element(s). Such a methodclaim should not be interpreted, for example, to encompass a method thatis performed mentally or by hand (e.g., using pencil and paper).Similarly, any product claim herein which recites that the claimedproduct includes a computer, a processor, a memory, and/or similarcomputer-related element, is intended to, and should only be interpretedto, encompass products which include the recited computer-relatedelement(s). Such a product claim should not be interpreted, for example,to encompass a product that does not include the recitedcomputer-related element(s).

In embodiments in which a classical computing component executes acomputer program providing any subset of the functionality within thescope of the claims below, the computer program may be implemented inany programming language, such as assembly language, machine language, ahigh-level procedural programming language, or an object-orientedprogramming language. The programming language may, for example, be acompiled or interpreted programming language.

Each such computer program may be implemented in a computer programproduct tangibly embodied in a machine-readable storage device forexecution by a computer processor, which may be either a classicalprocessor or a quantum processor. Method steps of the invention may beperformed by one or more computer processors executing a programtangibly embodied on a computer-readable medium to perform functions ofthe invention by operating on input and generating output. Suitableprocessors include, by way of example, both general and special purposemicroprocessors. Generally, the processor receives (reads) instructionsand data from a memory (such as a read-only memory and/or a randomaccess memory) and writes (stores) instructions and data to the memory.Storage devices suitable for tangibly embodying computer programinstructions and data include, for example, all forms of non-volatilememory, such as semiconductor memory devices, including EPROM, EEPROM,and flash memory devices; magnetic disks such as internal hard disks andremovable disks; magneto-optical disks; and CD-ROMs. Any of theforegoing may be supplemented by, or incorporated in, specially-designedASICs (application-specific integrated circuits) or FPGAs(Field-Programmable Gate Arrays). A classical computer can generallyalso receive (read) programs and data from, and write (store) programsand data to, a non-transitory computer-readable storage medium such asan internal disk (not shown) or a removable disk. These elements willalso be found in a conventional desktop or workstation computer as wellas other computers suitable for executing computer programs implementingthe methods described herein, which may be used in conjunction with anydigital print engine or marking engine, display monitor, or other rasteroutput device capable of producing color or gray scale pixels on paper,film, display screen, or other output medium.

Any data disclosed herein may be implemented, for example, in one ormore data structures tangibly stored on a non-transitorycomputer-readable medium (such as a classical computer-readable medium,a quantum computer-readable medium, or an HQC computer-readable medium).Embodiments of the invention may store such data in such datastructure(s) and read such data from such data structure(s).

What is claimed is:
 1. A method for generating a quantum contextualmeasurement from a quantum device capable of performing continuous timeevolution, the method comprising: (A) generating a first measurementresult, the generating comprising: (A) (1) initializing the quantumdevice to a first initial quantum state; (A) (2) applying, on thequantum device, a first continuous time evolution to the initial quantumstate to generate a first evolved state; and (A) (3) measuring the firstevolved state on the quantum device to generate the first measurementresult; (B) generating a second measurement result, the generatingcomprising: (B) (1) initializing the quantum device to a second initialquantum state; (B) (2) applying, on the quantum device, a secondcontinuous time evolution to the second initial quantum state togenerate a second evolved state which is at least approximately equal tothe first evolved state; (B) (3) applying, on the quantum device, athird continuous time evolution to the second evolved state to generatea third evolved state; and (B) (4) measuring the third evolved state onthe quantum device to generate the second measurement result; and (C)combining the first measurement result and the second measurement resultto generate the quantum contextual measurement.
 2. The method of claim1, wherein at least one of the first continuous time evolution and thesecond continuous time evolution is parameterized by a set ofparameters.
 3. The method of claim 2, further comprising: (D) providingan input into a generative neural network, wherein the input is afunction of the quantum contextual measurement.
 4. The method of claim2, further comprising: (D) tuning the set of parameters, based on anobjective function, to produce an updated set of parameters.
 5. Themethod of claim 4, wherein the second continuous time evolution ischosen such that measuring the third evolved state is equivalent to achange of basis on measuring the first evolved state.
 6. The method ofclaim 4, wherein measuring the third evolved state is equivalent to achange of basis on measuring the first evolved state.
 7. The method ofclaim 1, wherein the second continuous time evolution is chosen suchthat measuring the third evolved state is equivalent to a change ofbasis on measuring the first evolved state.
 8. The method of claim 1,wherein measuring the third evolved state is equivalent to a change ofbasis on measuring the first evolved state.
 9. The method of claim 1,wherein the quantum device comprises a quantum annealer.
 10. The methodof claim 1, wherein the second initial quantum state is at leastapproximately equal to the first initial quantum state.
 11. The methodof claim 10, wherein the second continuous time evolution is at leastapproximately equal to the first continuous time evolution.
 12. Themethod of claim 1, further comprising: (D) generating a plurality ofadditional measurement results wherein the generation of each additionalmeasurement results comprises: (D) (1) initializing the quantum deviceto an additional initial quantum state; (D) (2) applying, on the quantumdevice, a first additional continuous time evolution to the additionalinitial quantum state to generate a first additional evolved state whichis at least approximately equal to the first evolved state; (D) (3)applying, on the quantum device, a second additional continuous timeevolution to the first additional evolved state to generate a secondadditional evolved state; and (D) (4) measuring the second additionalevolved state on the quantum device to generate the additionalmeasurement result; and (E) combining the plurality of additionalmeasurement results to the quantum contextual measurement to generate anexpanded quantum contextual measurement.
 13. A hybrid quantum-classicalcomputing system for generating a quantum contextual measurement from aquantum device capable of performing continuous time evolution, thehybrid quantum-classical computing system including: the quantum device,comprising a plurality of qubits and a qubit controller that manipulatesthe plurality of qubits; and a classical computer including at least oneprocessor and at least one non-transitory computer-readable medium, theat least one non-transitory computer-readable medium having computerprogram instructions stored thereon, the computer program instructionsbeing executable by the at least one processor to cause the classicalcomputer to cooperate with the quantum device to perform a method, themethod comprising: (A) generating a first measurement result, thegenerating comprising: (A) (1) initializing the quantum device to afirst initial quantum state; (A) (2) applying, on the quantum device, afirst continuous time evolution to the initial quantum state to generatea first evolved state; and (A) (3) measuring the first evolved state onthe quantum device to generate the first measurement result; (B)generating a second measurement result, the generating comprising: (B)(1) initializing the quantum device to a second initial quantum state;(B) (2) applying, on the quantum device, a second continuous timeevolution to the second initial quantum state to generate a secondevolved state which is at least approximately equal to the first evolvedstate; (B) (3) applying, on the quantum device, a third continuous timeevolution to the second evolved state to generate a third evolved state;and (B) (4) measuring the third evolved state on the quantum device togenerate the second measurement result; and (C) combining the firstmeasurement result and the second measurement result to generate thequantum contextual measurement.
 14. The hybrid quantum-classicalcomputing system of claim 13, wherein at least one of the firstcontinuous time evolution and the second continuous time evolution isparameterized by a set of parameters.
 15. The hybrid quantum-classicalcomputing system of claim 14, wherein the method further comprises: (D)providing an input into a generative neural network, wherein the inputis a function of the quantum contextual measurement.
 16. The hybridquantum-classical computing system of claim 14, wherein the methodfurther comprises: (D) tuning the set of parameters, based on anobjective function, to produce an updated set of parameters.
 17. Thehybrid quantum-classical computing system of claim 16, wherein thesecond continuous time evolution is chosen such that measuring the thirdevolved state is equivalent to a change of basis on measuring the firstevolved state.
 18. The hybrid quantum-classical computing system ofclaim 16, wherein measuring the third evolved state is equivalent to achange of basis on measuring the first evolved state.
 19. The hybridquantum-classical computing system of claim 13, wherein the secondcontinuous time evolution is chosen such that measuring the thirdevolved state is equivalent to a change of basis on measuring the firstevolved state.
 20. The hybrid quantum-classical computing system ofclaim 13, wherein measuring the third evolved state is equivalent to achange of basis on measuring the first evolved state.
 21. The hybridquantum-classical computing system of claim 13, wherein the quantumdevice comprises a quantum annealer.
 22. The hybrid quantum-classicalcomputing system of claim 13, wherein the second initial quantum stateis at least approximately equal to the first initial quantum state. 23.The hybrid quantum-classical computing system of claim 22, wherein thesecond continuous time evolution is at least approximately equal to thefirst continuous time evolution.
 24. The hybrid quantum-classicalcomputing system of claim 13, wherein the method further comprises: (D)generating a plurality of additional measurement results wherein thegeneration of each additional measurement results comprises: (D) (1)initializing the quantum device to an additional initial quantum state;(D) (2) applying, on the quantum device, a first additional continuoustime evolution to the additional initial quantum state to generate afirst additional evolved state which is at least approximately equal tothe first evolved state; (D) (3) applying, on the quantum device, asecond additional continuous time evolution to the first additionalevolved state to generate a second additional evolved state; and (D) (4)measuring the second additional evolved state on the quantum device togenerate the additional measurement result; and (E) combining theplurality of additional measurement results to the quantum contextualmeasurement to generate an expanded quantum contextual measurement.